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Author : Henry Burchard Fine
Publisher :
ISBN 13 :
Total Pages : 154 pages
Book Rating : 4.A/5 ( download)
Download or read book The Number-system of Algebra Treated Theoretically and Historically written by Henry Burchard Fine and published by . This book was released on 1890 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Henry Burchard Fine
Publisher :
ISBN 13 :
Total Pages : 154 pages
Book Rating : 4.A/5 ( download)
Download or read book The Number-system of Algebra written by Henry Burchard Fine and published by . This book was released on 1890 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Henry Burchard Fine
Publisher :
ISBN 13 :
Total Pages : 132 pages
Book Rating : 4.:/5 (4 download)
Download or read book The Number System of Algebra Treated Theoretically and Historically written by Henry Burchard Fine and published by . This book was released on 1900 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Henry B Fine
Publisher :
ISBN 13 : 9781670763402
Total Pages : 106 pages
Book Rating : 4.7/5 (634 download)
Download or read book The Number-System of Algebra written by Henry B Fine and published by . This book was released on 2019-12-02 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: THENUMBER-SYSTEM OF ALGEBRATREATED THEORETICALLY AND HISTORICALLY
Author : Henry B. Fine
Publisher : Forgotten Books
ISBN 13 : 9781330109908
Total Pages : 149 pages
Book Rating : 4.1/5 (99 download)
Download or read book The Number-System of Algebra written by Henry B. Fine and published by Forgotten Books. This book was released on 2015-06-16 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from The Number-System of Algebra: Treated Theoretically and Historically The theoretical part of this little book is an elementary exposition of the nature of the number concept, of the positive integer, and of the four artificial forms of number which, with the positive integer, constitute the "number-system" of algebra, viz. the negative, the fraction, the irrational, and the imaginary. The discussion of the artificial numbers follows, in general, the same lines as my pamphlet: On the Forms of Number arising in Common Algebra, but it is much more exhaustive and thoroughgoing. The point of view is the one first suggested by Peacock and Gregory, and accepted by mathematicians generally since the discovery of quaternions and the Ausdehnungslehre of Grassmann, that algebra is completely defined formally by the laws of combination to which its fundamental operations are subject; that, speaking generally, these laws alone define the operations, and the operations the various artificial numbers, as their formal or symbolic results. This doctrine was fully developed for the negative, the fraction, and the imaginary by Hankel, in his Complexe Zahlensystemen, in 1867, and made complete by Cantor's beautiful theory of the irrational in 1871, but it has not as yet received adequate treatment in English. Any large degree of originality in work of this kind is naturally out of the question. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Author : Henry Fine
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (492 download)
Download or read book The Number-system of Algebra written by Henry Fine and published by . This book was released on 1937 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Henry Burchard Fine
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (914 download)
Download or read book The Number-System of Algebra (2nd Edition) written by Henry Burchard Fine and published by . This book was released on 2006 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Benjamin Fine
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (651 download)
Download or read book The Number System of Algebra Treated Theoretically and Historically written by Benjamin Fine and published by . This book was released on 1937 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : HENRY B. FINE
Publisher :
ISBN 13 : 9781033505786
Total Pages : 0 pages
Book Rating : 4.5/5 (57 download)
Download or read book NUMBER-SYSTEM OF ALGEBRA written by HENRY B. FINE and published by . This book was released on 2018 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Henry Burchard Fine
Publisher : Nabu Press
ISBN 13 : 9781289936525
Total Pages : 150 pages
Book Rating : 4.9/5 (365 download)
Download or read book The Number-System of Algebra written by Henry Burchard Fine and published by Nabu Press. This book was released on 2013-10 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a reproduction of a book published before 1923. This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book.
Author : Henry B Fine
Publisher :
ISBN 13 : 9781675384718
Total Pages : 96 pages
Book Rating : 4.3/5 (847 download)
Download or read book The Number-System of Algebra written by Henry B Fine and published by . This book was released on 2019-12-14 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theoretical part of this little book is an elementary exposition of the nature of the number concept, of the positive integer, and of the four artificial forms of number which, with the positive integer, constitute the \number-system" of algebra, viz. the negative, the fraction, the irrational, and the imaginary. The discussion of the artificial numbers follows, in general, the same lines as my pamphlet: On the Forms of Number arising in Common Algebra, but it is much more exhaustive and thorough-going. The point of view is the one first suggested by Peacock and Gregory, and accepted bymathematicians generally since the discovery of quaternions and the Ausdehnungslehre of Grassmann, that algebra is completely defined formally by the laws of combination to which its fundamental operations are subject; that, speaking generally, these laws alone define the operations, and the operations the various artificial numbers, as their formal or symbolic results. This doctrine was fully developed for the negative, the fraction, and the imaginary by Hankel, in his Complexe Zahlensystemen, in 1867, and made complete by Cantor's beautiful theory of the irrational in 1871, but it has notas yet received adequate treatment in English.
Author : Henry B. Fine
Publisher : Createspace Independent Publishing Platform
ISBN 13 : 9781544999647
Total Pages : 104 pages
Book Rating : 4.9/5 (996 download)
Download or read book The Number-System of Algebra (2nd Edition) written by Henry B. Fine and published by Createspace Independent Publishing Platform. This book was released on 2017-04-15 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Number-System of Algebra (2nd edition) by Henry B. Fine
Author : Henry B Fine
Publisher :
ISBN 13 : 9781087313221
Total Pages : 96 pages
Book Rating : 4.3/5 (132 download)
Download or read book Number-System of Algebra written by Henry B Fine and published by . This book was released on 2019-08-04 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theoretical part of this little book is an elementary exposition of the nature ofthe number concept, of the positive integer, and of the four artificial forms of numberwhich, with the positive integer, constitute the \number-system" of algebra, viz. thenegative, the fraction, the irrational, and the imaginary. The discussion of the arti ̄cialnumbers follows, in general, the same lines as my pamphlet: On the Forms of Numberarising in Common Algebra, but it is much more exhaustive and thorough-going. Thepoint of view is the one ̄first suggested by Peacock and Gregory, and accepted bymathematicians generally since the discovery of quaternions and the Ausdehnungslehreof Grassmann, that algebra is completely de ̄ned formally by the laws of combinationto which its fundamental operations are subject; that, speaking generally, these lawsalone define the operations, and the operations the various artificial numbers, as theirformal or symbolic results. This doctrine was fully developed for the negative, thefraction, and the imaginary by Hankel, in his Complexe Zahlensystemen, in 1867, andmade complete by Cantor's beautiful theory of the irrational in 1871, but it has notas yet received adequate treatment in English.
Author : Mark Burgin
Publisher : World Scientific
ISBN 13 : 9811236852
Total Pages : 370 pages
Book Rating : 4.8/5 (112 download)
Download or read book Trilogy Of Numbers And Arithmetic - Book 1: History Of Numbers And Arithmetic: An Information Perspective written by Mark Burgin and published by World Scientific. This book was released on 2022-04-22 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is the first in the trilogy which will bring you to the fascinating world of numbers and operations with them. Numbers provide information about myriads of things. Together with operations, numbers constitute arithmetic forming in basic intellectual instruments of theoretical and practical activity of people and offering powerful tools for representation, acquisition, transmission, processing, storage, and management of information about the world.The history of numbers and arithmetic is the topic of a variety of books and at the same time, it is extensively presented in many books on the history of mathematics. However, all of them, at best, bring the reader to the end of the 19th century without including the developments in these areas in the 20th century and later. Besides, such books consider and describe only the most popular classes of numbers, such as whole numbers or real numbers. At the same time, a diversity of new classes of numbers and arithmetic were introduced in the 20th century.This book looks into the chronicle of numbers and arithmetic from ancient times all the way to 21st century. It also includes the developments in these areas in the 20th century and later. A unique aspect of this book is its information orientation of the exposition of the history of numbers and arithmetic.
Author : Henry B. (Henry Burchard) 1858-19 Fine
Publisher : Wentworth Press
ISBN 13 : 9781371850937
Total Pages : 148 pages
Book Rating : 4.8/5 (59 download)
Download or read book NUMBER-SYSTEM OF ALGEBRA written by Henry B. (Henry Burchard) 1858-19 Fine and published by Wentworth Press. This book was released on 2016-08-28 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Author : Henry Fine
Publisher :
ISBN 13 : 9781490505015
Total Pages : 94 pages
Book Rating : 4.5/5 (5 download)
Download or read book The Number System of Algebra written by Henry Fine and published by . This book was released on 2013-06-23 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt: I THEORETICAL1 THE POSITIVE INTEGER, AND THE LAWS WHICH REGULATE THE ADDITION AND MULTIPLICATION OF POSITIVE INTEGERS The number concept Numerical equality Numeral symbols The numerical equation Counting Addition and its laws Multiplication and its laws 2 SUBTRACTION AND THE NEGATIVE INTEGER Numerical subtraction Determinateness of numerical subtraction Formal rules of subtraction Limitations of numerical subtraction Symbolic equations Principle of permanence. Symbolic subtraction Zero The negative Recapitulation of the argument of the chapter 3 DIVISION AND THE FRACTION Numerical division Determinateness of numerical division Formal rules of division Limitations of numerical division Symbolic division. The fraction Negative fractions General test of the equality or inequality of fractions Indeterminateness of division by zero Determinateness of symbolic division The vanishing of a product The system of rational numbers 4 THE IRRATIONAL Inadequateness of the system of rational numbers Numbers defined by regular sequences. The irrational Generalized definitions of zero, positive, negative Of the four fundamental operations Of equality and greater and lesser inequality The number defined by a regular sequence its limiting value Division by zero The number-system defined by regular sequences of rationals a closed and continuous system 5 THE IMAGINARY COMPLEX NUMBERS The pure imaginary Complex numbers The fundamental operations on complex numbers Numerical comparison of complex numbers Adequateness of the system of complex number Fundamental characteristics of the algebra of number 6 GRAPHICAL REPRESENTATION OF NUMBERS THE VARIABLE. Correspondence between the real number-system and the points of a line The continuous variable Correspondence between the complex number-system and the points of a plane The complex variable Definitions of modulus and argument of a complex number and of sine, cosine, and circular measure of an angle Construction of the points which represent the sum, difference, product, and quotient of two complex numbers 7 THE FUNDAMENTAL THEOREM OF ALGEBRA Definitions of the algebraic equation and its roots Demonstration that an algebraic equation of the nth degree has n roots 8 INFINITE SERIES8.1 REAL SERIES Definitions of sum, convergence, and divergence General test of convergence Absolute and conditional convergence Special tests of convergence Limits of convergence The fundamental operations on infinite series 8.2 COMPLEX SERIES General test of convergence Absolute and conditional convergence The region of convergence A theorem respecting complex series The fundamental operations on complex series 9 THE EXPONENTIAL AND LOGARITHMIC FUNCTIONS UNDETERMINED COEFFICIENTS. INVOLUTION AND EVOLUTION. THE BINOMIAL THEOREM Definition of function Functional equation of the exponential function Undetermined coefficients The exponential function The functions sine and cosine Periodicity of these functions The logarithmic function Indeterminateness of logarithms Permanence of the laws of exponents Permanence of the laws of logarithms Involution and evolution The binomial theorem for complex exponents II HISTORICAL10 PRIMITIVE NUMERALS Gesture symbols Spoken symbols Written symbols 11 HISTORIC SYSTEMS OF NOTATION Egyptian and Phoenician Greek Roman Indo-Arabic 12 THE FRACTION Primitive fractions Roman fractions Egyptian (the Book of Ahmes) Babylonian or sexagesimal Greek 13 ORIGIN OF THE IRRATIONAL Discovery of irrational lines. Pythagoras Consequences of this discovery in Greek mathematics Greek approximate values of irrationals 14 ORIGIN OF THE NEGATIVE AND THE IMAGINARY.15 ACCEPTANCE OF THE NEGATIVE16 RECOGNITION OF THE PURELY SYMBOLIC CHARACTERS OF ALGEBRA
Author : William Aspray
Publisher : U of Minnesota Press
ISBN 13 : 0816615675
Total Pages : 396 pages
Book Rating : 4.8/5 (166 download)
Download or read book History and Philosophy of Modern Mathematics written by William Aspray and published by U of Minnesota Press. This book was released on 1988 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: History and Philosophy of Modern Mathematics was first published in 1988. Minnesota Archive Editions uses digital technology to make long-unavailable books once again accessible, and are published unaltered from the original University of Minnesota Press editions. The fourteen essays in this volume build on the pioneering effort of Garrett Birkhoff, professor of mathematics at Harvard University, who in 1974 organized a conference of mathematicians and historians of modern mathematics to examine how the two disciplines approach the history of mathematics. In History and Philosophy of Modern Mathematics, William Aspray and Philip Kitcher bring together distinguished scholars from mathematics, history, and philosophy to assess the current state of the field. Their essays, which grow out of a 1985 conference at the University of Minnesota, develop the basic premise that mathematical thought needs to be studied from an interdisciplinary perspective. The opening essays study issues arising within logic and the foundations of mathematics, a traditional area of interest to historians and philosophers. The second section examines issues in the history of mathematics within the framework of established historical periods and questions. Next come case studies that illustrate the power of an interdisciplinary approach to the study of mathematics. The collection closes with a look at mathematics from a sociohistorical perspective, including the way institutions affect what constitutes mathematical knowledge.
